Math Recovery Curriculum

Curiosity Corner

10–15 min DOK 2

Teacher Setup

"I'm going to show you something for just one second. Don't count — just look." Flash the five-frame for 1–2 seconds, then cover it. Ask: "How many did you see? How did your brain know without counting?" Let 3–4 students share. Some will say they counted fast. Some will say they just knew. Create genuine tension: "Wait — how is that possible? Can your brain really see a number without counting?" Write their theories on the board.

Closing the Hook

"That's exactly what mathematicians call subitizing — and today we're going to figure out how your brain does it."

Student Discussion Prompts

"Did anyone see it differently?" "Did anyone count?" "Did anyone not need to count?"

What You Might Notice (Math Recovery Stages)

Perceptual

Student counts all dots one by one

What This Means

Student has not yet developed figurative imagery — they need the physical dots present to quantify. This is expected at the start of first grade.

What To Do Next

Flash the card more briefly (under 1 second) to make counting impossible. Say: "This time your brain has to see it — no counting allowed." Repeat with 2 and 3 dots to build confidence with smaller quantities first.

Figurative

Student instantly says 3 or 4 without counting

What This Means

Student has internalized spatial patterns for these quantities. They can subitize perceptually but may not yet decompose flexibly.

What To Do Next

Push toward part-part-whole: "You saw 4 — did you see it as two groups? Could you see it as 3 and 1? As 2 and 2?" This student is ready for the emerging stage work.

Part-Part-Whole Emerging

Student describes "I saw 3 and 1 more"

What This Means

This is your highest-level entry point. Student is beginning to decompose quantities flexibly — the foundation of additive reasoning.

What To Do Next

Name this publicly: "Did everyone hear what said? They saw it in two parts." Ask: "Could you see the same number a different way? What other parts could you find?" Begin connecting to number sentences if appropriate.

Perceptual

Student uses fingers to track while counting

What This Means

Student is using finger tracking as a physical substitute for the visual stimulus — still relying on perceptual counting strategies rather than pattern recognition.

What To Do Next

Try putting hands in lap before flashing. Ask: "What did you picture in your head after I covered it?" Shift focus from counting accuracy to mental imagery development.

Number Routines

10–12 min DOK 1–2

Note

See the Calendar Math panel in the right sidebar for the full flexible routine. This section may be used as a brief bridge between Curiosity Corner and Core Instruction, or omitted if Calendar Math was done earlier.

"We just saw how our brains can see numbers without counting. Let's practice with our number routines — and notice when your brain already knows the answer before you finish counting."

Core Instruction

15–20 min DOK 2

Teacher Modeling Block

Opening Move — Model Uncertainty First

Show a five-frame with 5 dots for 3 seconds, cover it. Ask: "What did you see? Turn and tell your partner." Collect 2–3 responses. Then reveal it again. Say: "I want to think about what my brain did. I didn't count 1, 2, 3, 4, 5 — I think I saw... hmm. Did anyone else see it in parts?"

Show for 3 seconds, then cover. Students draw what they saw before you reveal.

Think Aloud Script (after student sharing)

"Some of us saw 3 and 2 more. Some saw a full row. Both of those are ways our brain structures a number — and that's faster and smarter than counting every single dot."

Second Frame — Show 4 Dots

This time, show the frame, cover it, and ask students to draw what they saw on their whiteboards before you reveal. This forces internal visualization before confirmation.

"What do you see?"

Guided Practice Cards

Flash each card in sequence: show, cover, draw, share, justify. Card 4 (unstructured) is the transfer challenge — can students apply their strategy when dots aren't in a neat row?

Card 1 — 2 Dots

"How many?" "How do you know?"

Card 2 — 5 Dots

"How many?" "How do you know?"

Card 3 — 4 Structured

"How many?" "How do you know?"

Card 4 — 3 Unstructured ★ Transfer

"How many?" "How do you know?"

Student Work Time

15–20 min DOK 2 → 3

Shared Goal

Show a number two different ways and explain which way was easier for your brain to see.

Task Options

Option A

Build It

Use a five-frame mat and counters to build a number, then draw both arrangements on recording sheet.

Option B

Draw It

Draw two arrangements of the same number on dot paper without the frame. Show your brain's two ways.

Option C

Explain It

Choose any number 1–5, draw it two ways, and write: "My brain saw and more. That's total."

Differentiation

With Supports

5-frame mat · Counters · Dot cards 1–5 available as reference

Reduced Supports

Dot cards only · No frame mat · Draw on plain paper

Advanced

"How many to make 5?" · Find all possible ways to show a given number · Write a number sentence

Conferencing Guide

"You counted — what would happen if you tried to see it instead?"

Why Ask This

Creates productive disruption for a student still in the perceptual stage. Names their current strategy without judgment and invites a more sophisticated one.

What To Listen For

Student attempts to describe a spatial arrangement or hesitates — either response signals movement beyond count-all.

"Show me how you saw it — can you cover it and redraw it from memory?"

Why Ask This

Visualization without the stimulus present is a key indicator of figurative thinking. This separates pattern-matching from internalized quantity imagery.

What To Listen For

Draws with confidence and spatial accuracy = figurative stage emerging. Draws tallies or counts while drawing = still perceptual.

"Is there another way your brain could have seen the same number?"

Why Ask This

Pushes students who already subitize toward flexible part-part-whole thinking — the foundation of addition and subtraction reasoning.

What To Listen For

Student names two distinct decompositions ("I saw 3 and 1, but I could also see 2 and 2") — highest-level response, worth naming publicly.

"Which arrangement was easier to see? Why do you think that is?"

Why Ask This

Metacognitive prompt that builds mathematical communication and helps students articulate why structure matters — connecting to the lesson's core idea.

What To Listen For

Student references grouping, symmetry, or familiarity ("the row was easier because I know what 3 looks like") rather than just "I don't know."

"What if I moved one dot — would that change how you see it?"

Why Ask This

Probes whether subitizing is tied to a specific spatial arrangement or genuinely flexible. Students at figurative stage often lose confidence when dots shift.

What To Listen For

Student reasons that quantity is stable regardless of arrangement — conservation of number emerging. A significant developmental milestone worth noting.

Small Group Pullout Note

If 3+ students are consistently counting all dots (perceptual stage, cherry red in diagnostic tool), pull for focused small group work with 1–3 dot quantities only. Flash at 0.5 seconds and ask students to hold up fingers before revealing. This builds figurative imagery through rapid repeated exposure.

Differentiation Matrix

If Student...	Then Try...
Counts all dots every time	Flash card briefly (1–2 sec), hide immediately. Repeat with 2 and 3 dots to build imagery.
Sees groups of 2 reliably	Ask: "How many more to make 5?" Begin connecting subitizing to missing-part thinking.
Instantly knows 5	Challenge: "Show me 5 a different way. Can you make 5 with 3 groups? 4 groups?"
Describes parts verbally	Introduce number sentence notation: "You said 3 and 1 — can you write that? 3 + 1 = "

Peer Talk Structure

Partner Protocol

Partner A: "I saw because ."

Partner B: "I saw it differently. I saw ."

Then switch. Partner B shares first on the next card.

Encourage students to use sentence stems from the ELL sidebar. All students benefit from the language scaffold.

Reflection & Exit Ticket

5–8 min DOK 2

Closing Discussion — Return to Anchor

"So — how does your brain see a number without counting? Did any of your theories from the beginning of class change?" Let 2–3 students respond, then connect their language back to the word subitize written on the board.

Exit Ticket — Transfer Task

Show a new arrangement students have not seen in the lesson today.

"How many? How did you know?"

Gitch.org Checkpoints

CP 1.1 — Student can identify a quantity on a five-frame (1–5) without counting all. Mark: Counting All / Saw a Group / Named Parts

gitch.org → Lesson 1-1 → Checkpoint 1 · Use exit ticket tally above

CP 1.2 — Student can explain how they saw the quantity using spatial language (e.g. "I saw a group," "it looked like "). Mark: Not Yet / Emerging / Secure

gitch.org → Lesson 1-1 → Checkpoint 2 · Assess during conferencing

Exit Ticket Live Tally

Tap the strategy each student used as you review their exit ticket.

Counted All

Saw a Group

Named Parts

Curiosity Corner

10–15 min DOK 2

Lesson Objective Students will use the structure of the ten-frame and the anchor of 5 to recognize quantities 6–10, applying the "5 and some more" strategy.

Anchor Phenomenon

Your brain already knows 5.
Can it use that to see 7?

Five-frame: 5 (full)

Ten-frame: 7

Flash 5 on the five-frame, then 7 on the ten-frame. "Did your brain use the full top row to help see 7?"

Teacher Setup

"Yesterday we learned our brain can subitize numbers to 5. Today I want to push that further — I want to see if your brain can use what it knows about 5 to see bigger numbers." Flash a full five-frame. "How fast did your brain know that? Now watch." Flash ten-frame with 7. "How many? How did your brain figure it out?" Listen for: "I saw 5 on top and 2 more." That's the strategy — 5 and some more.

Student Discussion Prompts

"Did you see 5 first, then count on?" "What's the top row doing for your brain?" "Could you do this without the frame?" "What's 5 and 3 more?"

What You Might Notice

Perceptual

Student counts all dots from 1 even on ten-frame with full top row

What This Means

Student hasn't yet connected the full top row to the anchor quantity of 5. They're treating each dot as independent rather than seeing the row as a unit.

What To Do Next

Ask: "How many are in the top row?" (5) "So if I see the top row full and 2 more on the bottom, what's the fast way to know?" Scaffold the "5 and some more" language explicitly before independent work.

Figurative

Student sees top row as 5 but counts on from there by ones

What This Means

Student is using a counting-on strategy from 5 — this is transitional and productive. The goal is to move toward seeing the bottom quantity as a subitized unit rather than counted one by one.

What To Do Next

Ask: "You counted on from 5 — nice. Now look at the bottom row: can you see how many without counting?" If they can subitize small quantities (1–3) on the bottom, they're ready to combine: "5 and 2 — your brain can just know that's 7."

Part-Part-Whole Emerging

Student says "5 on top, 2 on the bottom — that's 7" without counting

What This Means

Student is decomposing numbers within 10 using the anchor of 5 — this is the target strategy for this lesson and the foundation of all ten-frame work to come.

What To Do Next

Push toward the full complement: "How many more to fill the whole frame? So 7 and make 10?" Begin connecting to "how many to make 10" — this student is ready for that extension.

Number Routines

10–12 min DOK 1–2

"As we do our routines today, notice — does your brain subitize any of the numbers we see? Where do you see five-frames or ten-frames hidden in our classroom?"

Connection Prompt

During Days in School: point out that the tally marks are grouped in fives — just like a five-frame. "We're already using this structure everywhere."

Core Instruction

15–20 min DOK 2

Introducing the Ten-Frame

Teacher Modeling

"You already know this frame — the top row is just our five-frame from yesterday. Watch what happens when I fill the whole top row." Fill 5. "How many? Good — 5. Now watch." Add 3 more to bottom row. "How many now? I'm not going to count — I'm going to use 5." Think aloud: "I see 5 on top. I see 3 on the bottom. 5 and 3 — that's 8. My brain used 5 as an anchor." That's our strategy today: 5 and some more.

Guided Practice — Flash Sequence

Flash each card for 2 seconds. Students write their answer on whiteboards before reveal. Push the strategy: "Did you see 5 first? What was on the bottom?"

Card 1 — 6 on Ten-Frame

"5 and how many more? What's the total?"

Card 2 — 8 on Ten-Frame

"5 and 3 more. Did your brain go straight to 8?"

Card 3 — 7 on Ten-Frame

"How many empty? How many to make 10?"

Card 4 — 9 on Ten-Frame ★

"Almost full — how many to make 10?"

Student Work Time

15–20 min DOK 2→3

Shared Goal

Build a number 6–10 on a ten-frame. Tell your partner: "I see 5 and more. That's ." Then show how many more to make 10.

With Supports

Use 6 or 7 · Pre-filled top row on mat (5 printed dots) · Student adds bottom row counters only · Sentence frame provided

Reduced Supports

Choose any number 6–10 · Draw own ten-frame · Write: " is 5 and "

Advanced

Show two numbers that add to 10 on separate ten-frames · Write the equation · "Can you find all the pairs that make 10?"

Conferencing Guide

"Point to the empty spaces — what do they tell you?"

Why Ask This

Shifts student attention from dots to the structure of the frame — including what's missing. This is the foundation of part-part-whole and missing-addend thinking.

What To Listen For

Student articulates "there are 2 empty" or "I need 2 more to fill it" — this shows they're reading the frame as a structure, not just a container.

"Can you show me the same number starting from a different spot?"

Why Ask This

Tests whether the student understands the convention (fill left to right) versus quantity. Disrupting the convention reveals whether they truly understand the frame's purpose.

What To Listen For

Student still gets the same total but notices it "looks different" — this is productive confusion worth discussing with the group.

"Which frame felt faster — five or ten? Why do you think that is?"

Why Ask This

Metacognitive prompt connecting Day 1 and Day 2. Students who say "five-frame was faster because it's smaller" are developing frame literacy.

What To Listen For

Any reference to familiarity, size, or the position of dots relative to the frame boundary — all signal emerging structural reasoning.

Small Group Note

Students still counting all on the five-frame should not move to the ten-frame independently. Work with them on five-frame subitizing with 1–3 dots before introducing the second frame.

Partner Protocol

Partner A: "I showed on the five-frame. My brain saw ."

Partner B: "On the ten-frame I saw . The empty spaces told me ."

Use ELL sentence stems from left sidebar throughout.

Reflection & Exit Ticket

5–8 min DOK 2

Closing Discussion

"So — does the frame matter? Would your brain see the number the same way if the dots were just floating around with no frame at all?" Let 2–3 students respond. Connect: "The frame gives your brain a structure to work with. That's why mathematicians invented it."

Exit Ticket

Show 8 on a ten-frame. How many empty spaces? How many more to make 10?

"Draw it. Then write: 8 is 5 and . I need more to make 10."

Gitch.org Checkpoints

CP 1.3 — Student uses "5 and some more" strategy to identify quantities 6–10 on a ten-frame without counting all. Mark: Counts All / Counts On From 5 / 5-and-Some-More Instant

gitch.org → Lesson 1-2 → Checkpoint 1 · Use exit ticket tally above

CP 1.4 — Student identifies how many more to make 10 for a given quantity (6–9). Mark: Not Yet / Emerging / Secure

gitch.org → Lesson 1-2 → Checkpoint 2 · Assess during exit ticket

Exit Ticket Live Tally

How did students show 8? What strategy did they use?

Counted All

Counted On From 5

5 and Some More (instant)

Curiosity Corner

10–15 min DOK 2

Teacher Setup

"Yesterday we learned that numbers above 5 are just 5 and some more. Today we're going to use that to find all the ways to make 10." Place 10 two-color counters in a row — 5 red, 5 yellow. "I have 10. Watch what I do." Slide 6 to one side, 4 to the other. "Still 10 — but now I see two parts: 6 and 4. Does your brain see it?" Flip some counters to show color-based decomposition. Record bonds: 10 = 5+5, 10 = 6+4, 10 = 7+3. "Let's find them all."

Student Discussion Prompts

"Is 6 and 4 the same as 4 and 6?" "What two numbers always add to 10?" "What if one part is 0? Is 10 and 0 still valid?" "Which pair was easiest to see on the ten-frame?"

What You Might Notice

Perceptual

Student re-counts after each split to verify total

What This Means

Student doesn't yet trust that quantity is conserved when objects are rearranged — still needs perceptual verification after every move.

What To Do Next

Before splitting, ask student to count and confirm: "We have 5. Now watch — I'm not adding or taking away, just moving." After split: "Did we add any? Did we take any away? So how many do we still have?" Build trust in conservation before pushing decomposition.

Figurative

Student finds 1–2 ways to break 5 and stops

What This Means

Student understands the concept but hasn't yet developed the systematic flexibility to find all combinations. Ready for guided extension.

What To Do Next

Ask: "You found 2 and 3. What if the first part was 1 instead? What would the second part be?" Walk them through a systematic approach: start with 1, increase by 1 each time.

Part-Part-Whole Emerging

Student finds multiple ways and notices a pattern

What This Means

Student is beginning to see decomposition as a system — a significant cognitive leap toward additive reasoning.

What To Do Next

Name it publicly: "Did you notice what did? As one part went up by 1, the other went down by 1. Does that always happen?" Introduce number bond notation if appropriate.

Number Routines

10–12 min DOK 1–2

"During routines today, see if you can spot any numbers that are hiding two parts inside them."

Core Instruction

15–20 min DOK 2

Number Bond Introduction

Teacher Modeling

"You already know number bonds from yesterday. Today we're going to use them for a bigger number — 10." Draw a number bond with 10 as the whole. "I'm going to use my ten-frame to help." Show 6 on a ten-frame. "I see 5 on top and 1 more on the bottom. Wait — that's only 6. Let me add one more." Fill to 7. "Now I see 5 and 2. That means 10 = 7 and 3. Let me show that as a bond." Fill in 7 and 3. "Every time I know how many I have, I can figure out the partner that makes 10. Let's find them all."

Finding All the Ways — Guided Discovery

Work through systematically as a class. Record each bond on the board. Ask students to predict the next one before you build it.

Part 1	Part 2	Whole	Student Prediction?
0	10	10	Start here — "what if one part is nothing?"
1	9	10	"If I move one over, what happens?"
2	8	10	"What's 2 and 8? Does your brain just know?"
3	7	10	Most students predict this one correctly
4	6	10	Students begin noticing the +1/−1 pattern
5	5	10	"The middle — both parts are equal!"
6	4	10	"Wait — is this different from 4 and 6?"
7	3	10	Students see the mirror pattern emerging
8	2	10	"We're going back down — do you see why?"
9	1	10	Students should predict this before you show it
10	0	10	"Back to 0 on the other side — it's symmetrical!"

Student Work Time

15–20 min DOK 2→3

Shared Goal

Find all the ways to make 10. Show each way with two-color counters on a ten-frame AND as a number bond. Can you find them all?

With Supports

Two-color counters · Pre-printed ten-frame and number bond templates · Teacher assigns 3–4 bonds to find rather than all 11

Reduced Supports

Find all bonds for 10 independently · Draw own bonds · Record as number sentences

Advanced

Find all 11 bonds · Explain the pattern in writing · "If I know 7+3=10, what do I automatically know?" (inverse: 10−7=3, 10−3=7)

Conferencing Guide

"How do you know you've found them all?"

Why Ask This

Pushes students from finding some combinations to thinking systematically — a major mathematical habit of mind.

What To Listen For

Student references a system ("I started at 0 and kept adding 1") versus a gut feeling ("I think that's all"). Either answer opens a productive conversation.

"If one part gets bigger by 1, what happens to the other part?"

Why Ask This

Introduces compensatory thinking — as one addend increases, the other decreases. This is a precursor to understanding the inverse relationship in addition and subtraction.

What To Listen For

"It gets smaller by 1" — this student is ready for explicit additive reasoning instruction.

"Does 1+4 look the same on a five-frame as 4+1?"

Why Ask This

Introduces the commutative property through a concrete, visual question before any formal notation. Students can see it's different visually but the same quantitatively.

What To Listen For

Student notices arrangement is different but total is the same — this is commutativity, named or not.

If Student...	Then Try...
Finds only 1–2 bonds and stops	Ask: "What if part 1 was 1? What would part 2 be?" Scaffold systematically from 0.
Lists bonds but not systematically	"Can you put them in order? What pattern do you notice?"
Notices 2+3 and 3+2 are both valid	Introduce: "Mathematicians call that the turn-around fact. Both are true!"
Finishes early	"Now try it for 4. Are there more ways or fewer ways than 5?"

Reflection & Exit Ticket

5–8 min DOK 2

Closing Discussion

"So — is there only one way to see a number? What did we discover today?" Push toward: numbers are flexible. 5 isn't just one thing — it's 2 and 3, it's 1 and 4, it's even 5 and 0. "That flexibility is what makes you powerful as a mathematician."

Exit Ticket

Complete the number bond. The whole is 10. One part is 6. What is the other part?

"Draw the bond. Show it on a ten-frame — 6 on one color, the other part on a second color."

Gitch.org Checkpoints

CP 1.5 — Student can find the missing part when given a whole (10) and one part, using a number bond or ten-frame. Mark: Counts All / Counts On / Known Fact

gitch.org → Lesson 1-3 → Checkpoint 1 · Use exit ticket tally above

CP 1.6 — Student can generate 3 or more number bonds for 10 systematically. Mark: Not Yet (1–2 bonds) / Emerging (3–5 bonds) / Secure (6+ bonds with pattern)

gitch.org → Lesson 1-3 → Checkpoint 2 · Assess during work time conferencing

Exit Ticket Live Tally

How did students find the partner to make 10?

Counted All From 1

Counted On From 6

Known Fact / Instant

Curiosity Corner

10–15 min DOK 2–3

Teacher Setup

"You've been building 6, 7, 8, 9, 10 on ten-frames. Today I want to know — could you show 8 WITHOUT a frame and still make it easy for someone's brain to see?" Flash: (1) 8 on a ten-frame, (2) 8 as a scattered pile, (3) 8 as two groups of 4. "Which one was fastest? What made it easy?" Push toward: the ten-frame works because it hides the parts inside the structure. "What if you designed your own structure that did the same thing?"

Discussion Prompts

"Could someone see 8 without counting in your design?" "Where does the '5 and some more' hide in your arrangement?" "Which numbers above 5 are hardest to arrange? Why?" "How is designing for 8 different from designing for 3?"

What You Might Notice

Perceptual

Student says "the frame one" but can't explain why

What This Means

Student perceives the difference but hasn't yet built language for spatial structure. The metacognitive language is the next step.

What To Do Next

Give them the language: "I think your brain likes the frame because the dots are in a line and you know where to look. Does that match what you felt?" Let students borrow your vocabulary before generating their own.

Figurative

Student says "because they're in a line" or "in a row"

What This Means

Student is articulating spatial reasoning — they're connecting arrangement to recognition speed. This is strong metacognitive thinking.

What To Do Next

Push further: "What about a triangle arrangement — is that structured? What about a circle?" Explore whether structure is about lines specifically or about predictability.

Part-Part-Whole Emerging

Student connects structure to the part-part-whole thinking from Day 3

What This Means

Student is integrating across lessons — connecting spatial structure to decomposition. This is exactly the synthesis this lesson is designed to build.

What To Do Next

Name this publicly and explicitly: "You just connected two things we've been learning — how we see numbers and how we break them apart. That's what mathematicians do."

Number Routines

10–12 min DOK 1–2

"Today during routines, I want you to notice: where do we see structured arrangements? Where do we see unstructured ones? Which ones does your brain know faster?"

Core Instruction

15–20 min DOK 2–3

Structured vs. Unstructured — Side by Side

Teacher Modeling

"I'm going to show you the same number — 8 — arranged four different ways. Brain speed rating after each one." Flash: (1) 8 on ten-frame, (2) 8 as two rows of 4, (3) 8 as a scattered pile, (4) 8 as 5 dots grouped + 3 dots grouped. Collect ratings. "Why was the grouped version fast? What did your brain do?" Guide toward: when you can see the 5 and the 3 separately, you don't need to count — your brain just adds two quantities it already knows.

Connecting to Addition

Bridge Prompt

"When you saw 8 as 5 and 3, you were doing something powerful: you were using a number you already knew — 5 — as an anchor to figure out a harder one. Write on board: 5 + 3 = 8. "That's what mathematicians do. They don't start from scratch every time — they build from what they know. And your brain has been doing it all week."

Student Work Time

15–20 min DOK 3

Shared Goal

Choose a number 6–10. Design your own arrangement that makes the "5 and some more" structure visible without a frame. Test it on your partner — can they see it without counting?

With Supports

Use 6 or 7 · Dot stickers in two colors — one for the group of 5, one for the "some more" · Teacher helps test with partner

Reduced Supports

Choose any number 6–10 · Draw on blank paper · Write the number sentence inside the design: 5 + =

Advanced

Design arrangements for two numbers that add to 10 · Show how both arrangements together make a full ten-frame · Write: " + = 10"

Conferencing Guide

"How did you decide on that arrangement? What were you thinking?"

Why Ask This

This is a design task — you want students articulating their spatial reasoning, not just producing an arrangement intuitively.

What To Listen For

Any reference to rows, lines, groups, or "looking like" a familiar pattern (dice, domino, frame) — all are signs of spatial reasoning development.

"Did your partner see it without counting? What did you change if they couldn't?"

Why Ask This

Iterative design thinking — if it didn't work, what did you revise? This mirrors real instructional design thinking applied to a math context.

What To Listen For

Student describes a revision ("I moved them into a line") — this is spatial problem-solving and worth naming publicly.

"Can you see any parts hiding inside your arrangement?"

Why Ask This

Bridges Days 3 and 4 — connecting spatial arrangement to part-part-whole decomposition. The arrangement a student designs often embeds a number bond they haven't made explicit.

What To Listen For

Student points to a natural grouping in their own design and names it as a part — "I see 2 here and 2 here, so it's 2 and 2."

Reflection & Exit Ticket

5–8 min DOK 3

Gallery Share

Post 4–5 student arrangements on the board (with permission). Flash each for 2 seconds. Ask: "Which one did your brain see fastest? What made it easy?" End with: "Tomorrow we're going to show everything we've learned this week — all of it in one place."

Exit Ticket

Draw 9 in an arrangement that makes "5 and some more" visible. Write the equation hiding inside it.

"My arrangement: [draw] · The equation: 5 + = 9 · How many more to make 10? "

Gitch.org Checkpoints

CP 1.7 — Student creates an arrangement for a number 6–10 that makes the "5 and some more" structure visible without a frame. Mark: No Structure / Structure Present / Structure + Labeled

gitch.org → Lesson 1-4 → Checkpoint 1 · Assess during work time

CP 1.8 — Student can write the equation hidden in their arrangement (5 + = ) and identify how many more to make 10. Mark: Not Yet / Emerging / Secure

gitch.org → Lesson 1-4 → Checkpoint 2 · Use exit ticket

Exit Ticket Live Tally

Did students make "5 and some more" visible in their design?

Arrangement Only, No Structure

Arrangement Shows 5 + Some More

Arrangement + Equation + Make 10

Curiosity Corner — Week Synthesis

10–12 min DOK 3

Lesson Objective Students will demonstrate subitizing and structural reasoning across quantities to 10 by producing multiple representations, explaining their thinking, and completing the week culminating task independently.

Week Reflection — Whole Class

Post the anchor chart from Day 1 (student theories about how the brain sees without counting). "Look at what you thought on Monday. What do you know now that you didn't know then?" Take 3–4 responses. Connect to each lesson: "Day 1 — we learned subitizing. Day 2 — we learned frames give our brain structure. Day 3 — we learned numbers can be broken into parts. Day 4 — we learned that arrangement matters. Today — you're going to show all of it."

"What's the most surprising thing you learned?" "What do you want to get better at?" "Where do you see these ideas outside math class?"

Number Routines

10–12 min DOK 1–2

"During routines today, see how many times you can catch your brain subitizing. Count them — we'll share after."

Student Work Time — Choice Task

20–25 min DOK 2–3

Open Task — Show What You Know

Choose any number 1–5. Show it as many ways as you can — five-frame, ten-frame, number bond, arrangement of your own design. Label each way and explain what you notice.

With Supports

Teacher assigns number (use 3 or 4) · Printed recording sheet with labeled boxes for each representation · Counters and mat available

Reduced Supports

Student chooses their number · Blank paper · At least 3 representations required

Advanced

Show the number all possible ways · Write a number sentence for every bond · Write one thing you notice about the pattern of bonds

Partner Share Before Culminating Task

Partner A: "I chose because . My favorite way to show it is because my brain sees it fastest."

Partner B: "Something I notice about your work is ."

This share happens before the culminating task — it helps students consolidate their thinking before working independently.

★

Culminating Task — Week 1 Skill Check

15–20 min · Individual · DOK 2–3

Teacher Setup

"Now it's time to show me what you've learned on your own. I'm going to give each of you a number card. This is your number — and I want to see everything your brain can do with it. No partner help, no counters — just you and what you know." Distribute number cards (differentiate by readiness: struggling students get 2 or 3, on-track get 4, advanced get 5).

Show What You Know — Recording Sheet

My number is: (circle: within 5 / within 10)

Part 1 — Five-Frame

Show your number on a five-frame

Part 2 — Your Choice

Show it a second way — ten-frame, number bond, or your own arrangement

Part 3 — Explain

"I know it's because "

★ Challenge

"How many more to make 10? + = 10"

Rubric — Use During Conferencing

Level	What It Looks Like	Next Steps
✓ Got It	Two distinct representations · Explanation references "5 and some more" or spatial structure (not counting) · Challenge question answered correctly · For within-10 numbers: uses ten-frame fluency	Ready for Unit 1 Week 2 — structuring to 20, skip counting
→ Getting There	Two representations but relies on counting on rather than "5 and some more" for numbers above 5 · Explanation references counting · Challenge question attempted but incorrect	Consolidate "5 and some more" strategy with ten-frame work in small group before Week 2
↻ Not Yet	Single representation · Counts all from 1 on numbers above 5 · Cannot explain reasoning · Challenge question skipped or answered by counting	Immediate small group — five-frame subitizing to 5 before returning to ten-frame work · Week 2 content on hold

Conferencing Guide — Culminating Task

"Tell me how you knew — without showing me your paper."

Why Ask This

The verbal explanation is your clearest window into whether subitizing is truly internalized or still dependent on the visual. A student who can describe what their brain did without looking at the paper has genuine figurative imagery.

What To Listen For

Spatial description without reference to counting ("I saw a row of 3 with one missing") = figurative or emerging. Counting description ("I went 1, 2, 3, 4") = still perceptual.

"What's the hardest part of this task for you right now?"

Why Ask This

Metacognitive awareness is a learning skill worth developing explicitly. Students who can identify their own difficulty are better positioned to improve.

What To Listen For

Any specific answer is useful data. "The explaining part" suggests language development needs. "The challenge question" suggests missing-addend work is needed.

Data Note — Use Rubric for Week 2 Grouping

Students scored "Not Yet" on this task should be pulled for a targeted small group at the start of Week 2 before the whole-class lesson begins. Students scored "Got It" with strong challenge question responses are ready for ten-frame structuring to 10.

Reflection & Week Close

8–10 min DOK 3

Week Close — Return to Day 1 Anchor

"On Monday I asked you: how does your brain know without counting? I wrote your theories on this chart." (Reveal Day 1 chart.) "Read them with me. Which ones were right? Which ones would you change now?" Take 3–4 responses. "On Monday, most of us were working with numbers like 3 and 4. By Friday, your brains were seeing 8, 9, and 10. You did that by using structure — using 5 as an anchor, using the frame to organize what you see. That's not just math — that's how mathematicians think."

Gitch.org Checkpoints — Week Summary

CP 1.9 — Culminating task: student produces two distinct representations of an assigned number and explains their reasoning without counting. Mark: Not Yet / Getting There / Got It

gitch.org → Lesson 1-5 → Checkpoint 1 · Use rubric scores from culminating task

CP 1.10 — Student answers the challenge question (how many more to make 10?) correctly. Mark: Not Yet / Correct · Use for Week 2 grouping

gitch.org → Lesson 1-5 → Checkpoint 2 · Cross-reference with Week Summary tally below

Culminating Task — Class Summary

Record rubric scores as you review tasks. Use for Week 2 grouping.

✓ Got It

→ Getting There

↻ Not Yet